Telephone Probability

Question 1

Assume that you are the owner of a small business that employs two people
on a telephone help desk. Records show that one of the employees is busy
taking calls for 40% or the time and the other is busy taking calls 55% of the
time:

a) What is the probability that when a new call comes in that both of the
employees are busy on the telephone?

b) What is the probability that at least one of the employees will be
available?

Question 2

Venture capital investments tend to be risky investments with a large
proportion of investments being unsuccessful. Suppose that you are the
manager of a venture capital firm with 20 investments. Assuming that it is
known that 70% of venture capital investments will be unsuccessful, determine
the following:

a) The probability that at least 5 of your investments will be successful.

b) The probability that no more than 15 will be unsuccessful.

Question 3

Suppose that 22% of employees in Australia intend to change employers over
the next two years. A company interested in reasons for their employee
turnover randomly samples a number of their employees:

a) If the company randomly samples 20 employees, find the probability
that exactly 4 of them will leave within two years.

b) For a random sample of 20 employees, find the mean, the variance
and the standard deviation for the number of employees that intend to
change employers of the next two years.